Chapter 6
1.
a. Δθ= θfθi= 178° 82°=
96°
b.180/π=96/x> x=
1.68 rad of flexion
2.
t= 0.8s, 3 rotations= 360°*3= 1080°
W= Δθ/Δt= 1080/0.8=
1350°/s
3.
Wi= 5 rad/s, Wf= 25rad/s, t= 1s
α=Δw/Δt= (255)/1=
20 rad/s/s in the direction of the spin
4.
r1= 1.5in, r2=15in, L1= 2in, L2=?
Θ= L1/r1= L2/r2> 2/1.5= L2/15>
L2= 20in
5.
W= 1700°/s= 29.67 rad/s, r= 1.2m, V=?, αr=?
a.
V= Wr= 29.67* 1.2=
35.6 m/s tangent to the circular path
b.
Αr= V²/r= 35.6²/1.2=
1056.4m/s² towards the axis
Make sure that you note that some of the equations use angular measures to
calculate linear measures. The answers to 5a and 5b are in m/s and m/s/s
which are linear.
6.
V1= 75m/s, L1= 5cm, L2= 100cm, V2=?
V=Wr= (Δθ/Δt)*r, Δθ1= Δθ2
and Δt1= Δt2> V1/V2= r1/r2
Θ= L1/r1= L2/r2> r1/r2= L1/L2
Therefore V1/V2= L1/L2 > 75/V2= 5/100>
V2= 1500cm/s
7.
Vball= 40m/s, dball= 17.50m, angular velocity of the bat= 12 rad, Δθ that the batter
needs to achieve if the bat is to be over home plate the same time as the ball = 1.51.8,
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 Summer '11
 Walsh
 Angular Momentum, 1.2m, home plate, Tom Waits, Θ= L1/r1= L2/r2

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